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Class 


The  Drop  Weight  of  the  Associated 

Liquids — Water,   Ethyl  Alcohol, 

Methyl  Alcohol  and  Acetic  Acid 


DISSERTATION 

SUBMITTED  IN  PARTIAL  FULFILMENT  OF  THE  REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY  OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 

A.  McD,  McAFKE,  B.A. 

NEW  YORK  CITY 
1911 


EASTON,  PA.: 

ESCHSNBACH  PRINTING  COMPANY. 
1911. 


The  Drop  Weight  of  the  Associated 

Liquids— Water,   Ethyl  Alcohol, 

Methyl  Alcohol  and  Acetic  Acid 


DISSERTATION 


SUBMITTED  IN  PARTIAL  FULFILMENT  OF  THE  REQUIRE- 
MENTS FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY 
IN  THE  FACULTY  OF  PURE  SCIENCE  IN  COLUMBIA 
UNIVERSITY  IN  THE  CITY  OF  NEW  YORK. 


BY 

A.  MCD.  MCAFEE,  B.A. 

NEW  YORK  CITY 


EASTON,  PA.: 

ESCHENBACH  PRINTING  COMPANY. 
1911. 


ACKNOWLEDGMENT. 

The  author  begs  to  thank  Professor  J.  Livingston  R. 
Morgan  for  his  advice,  assistance  and  encouragement,  with- 
out which  this  work  would  have  been  impossible. 


226929 


CONTENTS 

Introduction  and  Object  of  the  Investigation 5 

Experimental  Results 9 

Discussion  of  the  Results l% 

Summary. 22 


OBJECT  OF  THE  INVESTIGATION. 

According  to  Ramsay  and  Shields1  liquids  may  be  divided 
into  two  great  classes  —  the  so-called  non-associated  and 
associated  liquids,  the  former  following  the  law, 


where  by  definition 


The  associated  liquids  do  not  follow  this  law,  but  show 
different  values  for  K,  as  defined.  A  new  way  of  calculating 
K  is  soon  to  be  given  by  Morgan3  which  avoids  the  multiplica- 
tion of  error  inherent  in  this  equation.  In  brief,  this  method 
consists  in  rinding  once  for  all  a  value  of  K  from 

r(M/d)»  ==  KB   (288.5—  <  —  6), 

where  288.5  *s  the  observed  critical  temperature  of  ben- 
zene. Using  this  K  then  for  other  liquids  in 

r(M/d)»  =  KB(*C  —  *  —  6) 

he  shows  that  normal  molecular  weight  is  characterized  by 
the  giving  of  a  calculated  value  of  tc  which  is  independent 
of  the  temperature  of  observation.  An  associated  liquid 
then  is  one  which  does  not  give  the  same  calculated  tc  at  all 
temperatures  of  observation. 

Naturally,  this  is  just  what  is  contained  in  the  Ramsay 
and  Shields  relation,  only  removing  the  multiplication  of 
error  in  the  form  for  calculation, 

K  •= 


A* 

1  Z.  physik.  Chem,,  12,  433~475  (1893). 

2  f,  here,  is  the  surface  tension  in  dynes  per  centimeter,  M  the  molec- 
ular weight,  dt  and  d2  the  densities  at  the  temperature  tv  and  tv  tc  the 
critical  temperature  of  the  liquid  and  K  a  constant  with  a  mean  value 
2.12  ergs. 

3  May  Journal,  Jour.  Am.  Chem.  Soc.,  1911. 


It  has  been  shown  in  former  researches1  that  the  weight  of  a 
drop  cf  liquid,  falling  from  a  properly  constructed  tip,  is 
proportional  to  the  surface  tension  of  the  liquid.  It  has 
further  been  shown  that  for  all  non-associated  liquids  thus 
far  investigated,  falling  drop  weights  may  be  substituted 
for  surface  tensions  in  the  above  formula.  By  this  simple 
method,  surface  tensions,  molecular  weights  and  critical 
temperatures  of  the  non-associated  liquids  may  be  more 
easily  and  accurately  calculated  than  that  attained  by 
capillary  rise. 

The  object  of  the  present  investigation  was  to  apply  this 
method  of  falling  drop  weights  to  certain  typical  associated 
liquids  to  determine  whether  the  same  relations  obtain  with 
this  class  of  liquids  as  with  the  non-associated  ones.  The 
liquids  so  investigated  were  water,  ethyl  alcohol,  methyl 
alcohol  and  acetic  acid.  The  water  used  was  distilled  from 
potassium  dichromate  and  sulphuric  acid  and  then  redistilled 
with  a  little  barium  hydroxide.  The  alcohols  and  acetic 
acid  used  were  Kahlbaum's  "Special  K."  The  acid  was 
further  purified  by  freezing.  While  in  the  apparatus  they 
were  protected  from  any  moisture  by  suitable  drying  agents. 

The  apparatus  employed  together  with  the  thermostat  is 
the  same  as  that  recently  described  by  Morgan.2  It  was 
necessary  not  only  to  have  as  constant  temperature  as  possi- 
ble, but  to  have  also  a  wide  range  of  temperature;  the  thermo- 
stat described  by  him  fulfilled  both  these  requirements 
admirably,  and  also  permitted  a  quick  change  from  one 
temperature  to  another. 

Standardization  of  the  Tip. 

The  tip  used  in  this  work  was  approximately  5.530  mm. 
in  diameter.  The  first  requisite  was  the  standardization 
of  the  tip,  or,  in  other  words,  to  find  KB  in  the  formula 

1  Morgan  and  Stevenson,  Jour.  Am.  Chem.  Soc.,  30,  No.  3,  March, 
1908;  Morgan  and  Higgins,  Jour.  Am.  Chem.  Soc.,  30,  No.  7,  July,  1908. 

2  Jour.  Am.  Chem.  Soc.,  33,  No.  3,  March,  1911. 


288.5  —  (t  +  6) 

where  W  is  the  falling  drop  weight,  expressed  in  milligrams, 
of  the  liquid  at  the  temperature  t,  and  is  substituted  for 
surface  tension  in  the  formula  of  Eotvos  as  modified  by 
Ramsay  and  Shields,  i.  e., 

-TJT   __ 


Benzene  was  used  as  the  standardizing  liquid  with  the 
following  results: 

t.                Vessel +30  drops.  Vessel +5  drops.                              W. 

60.4°               9.4232  8.7888 

9.42305  8.7888   25.37 

60.4       9.4229  8.7888 

d.       W.        M.    (M/J)§      tc.  KB- 

60.4   0.83583   25.37      78   20.574    288.5       2.3502 

As  a  preliminary  check  on  this  KB  value,  quinoline  was 
observed  with  the  following  result. 

/,    Vesself  30  drops.  Vessel  (empty).  W. 

9.9561         8.6487  43.58 

60 . 3  9 . 9560 

d.        W.        M.    (MA*)3.       KB-     fc(calc.). 
60.3   I.06I49   43-58     129   24.536    2.3502   521.25 

As  Morgan  found  here  from  results  of  Morgan  and  Higgins1 
a  value  of  521.3  for  tc  this  value  of  KB  may  be  regarded  as 
satisfactory  and  will  be  used  throughout  this  work. 

As  already  alluded  to,  drop  weight  is  proportional  to 
surface  tension,  and  since 


=  2.3502  (tc  —  t  —  6) 
and 


1  Loc.  tit. 


or 


The  second  important  constant  to  be  determined  was 
therefore  the  one  necessary  for  the  correct  fulfilment  of  the 
Ramsay  and  Shields  formula.  Knowing  the  value  of  this 
constant,  surface  tension  from  drop  weight  can  be  immediately 
calculated  as  shown  above. 

As  has  already  been  indicated  the  value  of  this  constant 
is  approximately  2.12  ergs.  In  this  work,  the  average  K1 
from  the  benzene  values  of  Ramsay  and  Shields,  Ramsay 
and  Aston,  Renard  and  Guye  and  P.  Walden  has  been  taken 
as  being  nearest  the  truth. 

Ramsay  and  Shields  K  (from  benzene)  values  2  . 1012 
Ramsay  and  Aston  K  (from  benzene)  values  2.1211 
Renard  and  Guye  K  (from  benzene)  values  2  . 1 108 
P.  Walden  K  (from  benzene)  values  2 . 1260 

The  average  of  these  K  values  is  2.1148  which  is  used 
throughout  this  work. 

In  the  capillary  rise  method  rh  =  a2  (the  height  of  the 
liquid  in  a  capillary  of  i  mm.  radius).  For  purpose  of  com- 
parison it  was  thought  well  to  transform  drop  weight  into 
a2  values  also. 

Since  W  =  constant  -y 
** 

and     a2  =  constant  ~ 
a 

W 

a2  =  constant— r. 
a 

Knowing  the  density  and  drop  weight  of  a  liquid  at  any 
one  temperature  a2  is  thus  readily  calculated  by  the  em- 
ployment of  the  proper  constant. 

To  calculate  this  constant,  the  a2  values  for  benzene  ac- 
cording to  the  four  workers  above  referred  to  were  taken. 
Knowing  the  value  of  a2  and  the  value  of  W  at  the  corre- 
1  May  Journal,  Jour.  Am.  Chem.  Soc.,  1911. 


spending  temperature,  which  can  be  readily  calculated  from 
the  formula, 

w       2-35Q2  [288.5  — (*  + 6)] 

(7*\* 
UJ 

the  desired  constant  is  obtained. 

RAMSAY  AND  SHIELDS.  * 

t.         h.          r.          W.       a3.  K. 

80°     3.945    0.012935    22.75    5.104     0.18287 
90       3.772    0.012935    21.43    4.879     0.18308 

ioo  3-603       0.012935       20.14      4.662  0.18371 

RAMSAY  AND  ASTON.  2 

11. 2  3-642      0.01843        32-27      6.7122  0.18473 
46           3.213      0.01843        27.35       5-9216  0.18432 
78           2.810      0.01843        23.01       5.1789  0.18475 

RKNARD  AND  GUYK.S 

11.4       4.346      0.01522        32.25      6.6146  0.18217 

55.1       3-744      0.01522         26.10       5-6984  0.18376 

78.3  3-385   0.01522    22.97   5-I52o  0.18319 

P.  WALDKN.* 

18.1   3.392   0.0193     31.28   6.550    0.18446 
38-3   3-!57   0.0193     28.42   6.090    0.18417 

The  average  of  these  constants  (0.1838)  is  used  throughout 
this  work  for  transforming  drop  weight  into  a2  values, 

W, 

a]  =  0.1 838—. 
at 

EXPERIMENTAL  PART. 

Water. 

With  water  the  checks  at  times  were  very  much  poorer 
than  with  the  other  liquids.  This  may  be  due  to  impurity 
on  the  tip,  or  to  the  fact  that  the  drop  is  so  large  that  slight 
variations  may  occur  in  releasing  it.  In  every  case  every 
precaution  was  taken  to  remove  any  impurity  by  aid  of 
sulphuric  acid  and  bichromate. 

1  Loc.  cit. 

8  Z.  physik.  Chem.,  15,  I,  91. 

3  Jour.  d.  Chimie  Physique,  5,  92  (1907). 

4  Z.  Physik.  Chem.,  75,  568  (1910). 


10 

TABLE  i. 

Vessel,  Vessel, 

I.  30  drops.          Average.  10  drops.       Average.  W. 

o°    11.1770  94905 

11.1770   11.1770  94905    84.325 

11.1770  9-4905 

1.8   11.1697  9.4886 

11.1695         9.4886   84.045 

11.1693  9.4886 

4     11-1572  9-4844 

11.1572         9-48445  83.638 

11.1572  9-4845 

6     11.1459  9.4804 

11.14625         9.4804   83.293 

11.1466  9-4807 
9.4801 

7.5   11.1387  9-478i 

11.1382  9-478o 

11.1389  11.1385  9-4778  9-478o   83.027 

11-1385  9-478o 
11-1383 
11-1385 

12.95  i i. 1088  9.4678 

11.10845         9.4678   82.033 

11.1081  9-4678 


15     11.0973 

9 . 4640 
11.0964  11.09686  9.4640  81.643 

9 . 4640 
ii .0969 

17     11.0858          9.4605 

11.0862  11.08626         9-46045  81.291 
i i . 0868          9 . 4604 

19.25   11.0740          9  4556 

11.0740          9-4556   80.92 
11.0740 


II 

TABLE;  I. — (Continued}. 

Vessel,  Vessel, 

t.  30  drops.  Average.  10  drops.        Average.  W. 

22.5   11.0555  9-4495 

11.05565         9-4495   80.308 

11.0558  9-4495 

25.3   11.0422  9-4464 

11.04255         9-4465   79-803 

11.0429  9.4466 

27.81   11.0275  9 .4409 

11.0278         9.44105  79 .338 

11.0281  9-4412 

30     11.0174  9-4383 

11.0176  11.0172  9.4385  9-43847  78.937 

11.0166  9-4384 

36.46   10.9797  9-4252 

10.98005         9-42505  77-750 

10.9804  9 .4249 

40     10.9608  9 .4195 

10.9608          9.41936  77.072 

10.9608  9-4I93 

45     10.9323  9-4105 

10.9319         9-4Jo5   76.070 

10.9315  9  4I05 

55     10.8735 

9.3921 
10.8737  10.87346  9-3920  74-073 

9  3919 
10.8732 

60     10.8456  9-3825 

10.8456          9-38265  73-I48 

10.8456  9-3828 

70     10.7821  9-3604 

10.7820         9.36065  71.068 

.10.7819  9.3609 


t. 

77 


10 


20 


60 


70 


12 

I. — (Continued^). 


Vessel, 
50  drops. 

Average. 

Vessel,         Average. 
10  drops. 

w. 

0.7410 

9.3487 

0.7410 

10.7413 

9-3487 

69-63< 

o-74J9 

9-3487 

ETHYL  ALCOHOL. 

9.3168 
9.3168 
9.3168 

9.3168 

8  .  7988 
8  .  7988 
8  .  7988 

25.90 

9.3969 
9.3966 

9-39675 

8  .  8964 
8  .  8966 
8.8968 

25.01 

9.3702 
9.3702 

9.3702 

8.8878 
8.8878 
8.8878 

24.  12 

9-3I97 
9.3201 
9.3200 

9-3I993 

8.8735 
8-8734 
8.8733 

22.33 

9-2955 
9-2955 

9-2955 

8  .  8660 
8  .  86605 
8.8661 

21.47 

9.1663 
9.1656 
9.1660 

9.16596 

8-7537 
8.7538 
8-7539 

20.  6  1 

9.2613 
9.2616 

9  26145 

8-8575 
8.85745 
8-8574 

20.20 

9.2506 
9.2507 

9.25065 

8.8539 
8.8541 

8-8543 

19.83 

METHYL  ALCOHOL. 
9.4379  8.9104 

9.4383      9-4379      8.9100    8.91026     26.38 
9-4375  8.9104 


13 
TABLE  I. — (Continued'). 

t.  Vessel.  Average.  Vessel,         Average.  w 

30  drops.  10  drops 

20       9.3819  8.8918 

9.3822    9-38225  8.8917    24.53 

.  9.3826  8.8916 

30       9-3565  8.8846 

9-35665  8.8846    23.60 

9.3568  8.8846 

40      9-3300  8.8764 

9-32975         8-8765   22.66 

9-3295  8.8766 

50    9-3042  8.8694 

9-3045  9-3045  8.8694  8.8694  21.76 

9 . 3048  8 . 8694 


ACETIC  ACID. 

20      9-5445          8.9464 
9.5438          8.9464 

9.54417         8.9464   29.89 
9-5439          8.9464 
9-5445 

40      9.4820          8.9268 

9.4824   9.48246  8.9270  8.9270   27.77 
9.4830          8.9272 

60     9-4239          8.9100 

9.4243  9-4242         8.9100   25.71 

9.4244  8.9100 

70  9-396o  8.9023 

9.39625  8.90225     24.70 

9.3965  8.9022 

In  the  following  table  is  given  the  surface  tension  of  water 
at  intervals  from  o°-8o°  as  calculated  from  drop  weight 


which  is  multiplied  by  -       — .     Columns  4  and  5  contain  the 
2.3502 

values  for  surface  tension  of  water  at  intervals  from  o°-8o° 
by  the  method  of  capillary  rise.  Volkmann's  values1  from 
o°-40°  and  B runner's  values2  from  4O°-8o°  as  given  by 
Landolt,  Bornstein  and  Meyerhoffer,  Physikalisch  Chemische 
Tabellen,  p.  102,  are  contained  in  column  4.  Ramsay  and 
Shields'  values3  are  given  in  column  5. 

TABLE  2. 

(R.  &S.). 
73.21 


71-94 


70.60 
69. 10 

67.50 
65.98 

64.27 
62.55 

60.84 

In  Table  3  is  given  the  tc  of  water  as  calculated  from  drop 
weight  according  to  the  formula 

1  Ann.  d.  Physik.  u.  Chemie,  56,  457  (1895). 

2  Pogg.  Ann.,  70,  481  (1847). 

3  Z.  physik.  Chem.,  12,  433  (1893). 
*Read  from  curve. 


/. 

w. 

r- 

r  (v.  &B.) 

0° 

84-325 

75  88 

75  49 

'  1.8 

84.045 

75.63 

75-23 

4 

83.638 

75.26 

74.90 

6 

83  •  2.93 

74-95 

74.60 

7-5 

83.027 

74-71 

74-38 

10 

82.597* 

74  32 

74  oi 

12-95 

82.033 

73-8.2 

73-55 

15 

81.643 

73-46 

73-26 

17 

81  .291 

73-15 

72.96 

19-25 

80.920 

72.81 

72.63 

20 

80.760* 

72.67 

72  53 

22.5 

80  .  308 

72.26 

72-15 

25-30 

79.803 

71.81 

7i-73 

27.  8i 

79-338 

71-39 

71.36 

30 

78.937 

71.03 

71.03 

36.46 

77-750 

69.96 

70.02 

40 

77.072 

69  35 

69  54 

45 

76.070 

68.45 

68.60 

50 

75-152* 

67  63 

67.60 

55 

74-073 

66.65 

66.90 

60 

73  148 

65-82 

66.00 

70 

71.068 

63  95 

64.20 

77 

69.630 

62.66 

62  .90 

80 

69  .  ooo* 

62.09 

62.30 

W,(M/<y»  =  2.3502(^  —  ^  —  6) 
and  from  capillary  rise  according  to  the  formula 

*c  —  *  — 6) 


TABLE;  3. 


t. 

w. 

d.1 

W(M/<*)i. 

tc. 

0° 

84-325 

0.999868 

579-22 

252.45 

1.8 

84.045 

0.999961 

577-i6 

4 

83.638 

I  .  OOOOOO 

574-45 

254.42 

6 

83.293 

o  .  999968 

572.09 

255.42 

7-5 

83.027 

o  .  999902 

570.29 

256.16 

10 

82.597* 

0.999727 

567.40 

257  43 

12.95 

82.033 

0.999404 

563-65 

258.75 

15 

81.643 

0.999126 

561.07 

259-73 

17 

81  .291 

0.998970 

558.71 

260.73 

19  25 

80.920 

0.998382 

556.39 

262.00 

20 

80.760* 

0.998230 

555-34 

262  .  30 

22.5 

80  .  308 

0.997682 

552.43 

263  .  56 

25-30 

79.803 

o  .  996994 

549-21 

264.98 

27.8l 

79-338 

0.996316 

546  •  26 

266.24 

30 

78.937 

0.995673 

543  •  73 

267  .36 

36.46 

77-750 

0.993355 

536.38 

270.69 

40 

77.072 

0.992240 

532.li 

272.41 

45 

76.070 

0.990250 

525-90 

274.76 

50 

75-I52 

0.988070 

520.31 

277  39 

55 

74-073 

0.985730 

513-65 

279.56 

60 

73  •  H8 

0.983240 

508  .  10 

282  .  19 

70 

71.068 

0.977810 

495-47 

286.82 

77 

69.630 

0.973680 

486.82 

290.14 

80 

69  .  ooo 

0.971830 

483-03 

291  52 

r(M/d)f. 

r(M/<*)i. 

tc. 

tc. 

/. 

(V.  &B.). 

(R.  &S.). 

(V.&B.). 

(R.  &S.). 

0 

518.53 

502  .  90 

251.19 

243  .  80 

10 

508.41 

494-20 

256.41 

249.69 

20 

498  -  74 

485-30 

261.84 

255.48 

30 

489.27 

476.  10 

267.36 

26I.I3 

40 

480  .  i  i 

466  .  30 

273.02 

266.50 

50 

469.41 

456.40 

277.97 

27I.8I 

60 

458.44 

446  .  20 

282.78 

276.99 

70 

447  •  59 

436.00 

287-65 

282.01 

80 

436.12 

425.30 

292.22 

287.  10 

1  Landolt,  Bornstein  and  Meyerhoffer,  Tabellen,  p.  37. 
*Read  from  curve. 


i6 

In  Table  4  a  further  comparison  is  made  by  means  of  a8 
as  calculated  from  drop  weight  (a2  =  0.1838  W/d)  and 
a2  =  rh  observed  from  capillary  rise  by  Volkmann,  Brunner 
and  Ramsay  and  Shields. 

TABLE  4. 

02  aa  cfl 

t.  fromW.  (V.  &B.).  (R.  &S.). 

o°      15-501      I5-405      14.921 
10       15 -^S      I5-I03      14.664 

20  14.870  I4-823  14.412 

30  I4-572  I4-566  I4-I38 

40  I4-277  I4-295  13.860 

50  I3-980  I3-990  I3-605 

60  I3-674  I3-700  I3-3I4 

70        '   I3-358  I3-390  I3-032 

80  13.080  13.080  12.750 

TABLE  5. 

W(M/d)l.  W(M/d)f.  W(M/d)i. 

t.  Obs.  Calc.  Theoretical. 

o  579-22  578.96  579-22 

10  567-40  567-36  568.25 

20  555-34  555-65  556.98 

30  543-73  543-84  545-41 

40  532-11  531-93  533-53 

50  520.31  5I9-9I  521.35 

60  508.10  507.79  508.86 

70  495-47  495-57  496.08 

80  483-03  483-24  482.99 

In  the  following  tables  the  Ramsay  and  Shields  values 
have  been  calculated  from  the  equations  for  their  function 
values  as  derived  by  Morgan1.  With  acetic  acid  only  one 
determination  was  made  at  low  temperature  by  these  ob- 
servers, and,  as  was  pointed  out  in  the  article  just  referred 
to,  the  equation  for  acetic  acid  functions  does  not  give  good 
results  at  low  temperatures;  hence  the  values  given  here  for 
acetic  acid  from  capillary  rise  must  be  regarded  as  only 
approximate.  With  ethyl  alcohol  Timberg2  agrees  very 
closely  with  Ramsay  and  Shields. 

1  Jour.  Am.  Chem.  Soc.t  31,  309. 
*  Wied.  Ann.,  30,  545  (1887). 


TABLE  6. — ETHYL  ALCOHOL,  M  =  46,  tc  =  244. 


/. 

w. 

r- 

(R.&S.). 

Timberg. 

0° 

25-90 

23-3I 

23.80 

10 

25.01 

22.51 

22.90 

23-35 

20 

24.  12 

21  .70 

22.03 

22.  6l 

30 

23.27* 

20.94 

21  .  II 

21.63 

40 

22.33 

20.09 

20.20 

20.70 

50 

21.47 

19.32 

I9.3I 

19.82 

6o 

20.  61 

18.55 

18.43 

18-93 

65 

20.20 

18.18 

17.97 

18.05 

70 

I9-83 

17.84 

17.52 

TABLE  7. 


t. 

d. 

r  (M/d)a. 
W(M/<i)§.   (R.  &  S-). 

tc- 
from  W. 

tc. 

(R.  &  S.). 

O 

0 

o 

8095 

382 

.88 

350.2 

168 

•9 

171. 

6 

10 

0 

.8014 

372 

.  12 

340.5 

J74 

•4 

177. 

o 

20 

0 

.7926 

36i 

-56 

330.4 

179 

.8 

182. 

2 

30 

o 

.7840 

349 

•95 

319-9 

185 

-5 

I87. 

3 

40 

0 

7754 

339 

.61 

308.9 

190 

•  5 

192. 

i 

50 

0 

.7663 

329 

.20 

297.6 

196 

.  i 

I96. 

7 

60 

0 

7572 

3i8 

•47 

285.9 

201 

•5 

201  . 

2 

65 

0 

7523 

313 

•52 

279.9 

204 

•4 

203. 

3 

70 

o 

7474 

309 

.  12 

273.8 

207 

•4 

205. 

5 

TABLE 

8. 

/.        a2  from  W.     o 

:2(R.  &S.). 

a*  (Timberg). 

0° 

5 

.879 

6.180 

6 

.019 

10 

5 

•740 

6-035 

5 

.896 

20 

5 

•593 

5.890 

5 

•773 

30 

5 

•434 

5.601 

5 

-583 

40 

5 

•293 

5.3I3 

5 

.402 

50 

5 

.150 

5  -  HO 

5 

.252 

60 

5 

.003 

4.967 

5 

.070 

65 

4 

•933 

4-875 

4 

.978 

70 

4 

.871 

4-783 

4 

.886 

TABLE  9. — METHYL  ALCOHOL. 


w. 


r(R.  &S.).         a2  from  W.         a*  (R.  &  S.). 


0° 

26.38 

23-74 

24.36 

5.986 

6.  129 

10 

25-45* 

22.90 

23-50 

5.846 

5.986 

20 

24-53 

22.07 

23.02 

5-704 

5-937 

30 

23.60 

21  .24 

21.74 

5-540 

5.660 

40 

22.66 

20-39 

20.84 

5.378 

5.486 

50 

21  .76 

I9-58 

19  55 

5.228 

5.213 

*Read  from  curve. 


i8 
TABLE  10. 


f  (M/d)5. 

tc. 

*. 

d. 

w(M/<2)§. 

(R.  &S.). 

tc. 

(R.  &S.). 

0° 

O.SlOO 

306  .  oo 

282.66 

136.2 

139-7 

10 

0.8002* 

297.62 

274-77 

142  .6 

145-9 

20 

0.7905 

289.20 

271.40 

149.0 

154-3 

30 

0.7830 

280.01 

257-97 

i55-oo 

158.0 

40 

0-7745 

270.81 

249  .  06 

161  .2 

163.8 

50 

0.7650 

262.22 

235.60 

167.6 

167.4 

TABLE  n. — ACETIC  ACID. 

r.  r  (R.  &S.).1       a2  from  W.        a*(R.  &S). 


20° 

29.89 

26.90 

25.01 

5-237 

4.859 

30 

28.83* 

25-94 

23-87 

5-099 

4.682 

40 

27.77 

24.99 

23-49 

4-963 

4.656 

50 

26.74* 

24.01 

23.19 

4.830 

4.646 

60 

25-7I 

23-I4 

21-75 

4.697 

4.408 

70 

24.70 

22.23 

21  .OI 

4-563 

4-307 

TABLE  12. 

r(M/d)§.  *c.  tc. 

(R.  &  S.)-1  from  W.  (R.  &  S.).1 

20°   1.0491    443-70   371-2  214.8  201.5 

30    1.0392    430-67   356.6  219.3  204.6 

40    1.0284    417.74   348.8  223.7  210.9 

50    1-0175    405.10   340.6  228.4  217.0 

60    i. 0060    392-47   332.1  233.0  223.0 

70    0.9948    379-88   323.2  237.6  228.8 


Discussion  of  Results. 

As  has  already  been  shown,  surface  tension  as  calculated 
from  the  drop  weight  of  a  liquid  is  influenced  by  only  the 
drop  weight  of  the  liquid  and  the  density  of  benzene  from 
which  the  KB  values  are  calculated;  and  from  the  foregoing 
results  it  is  seen  with  what  extreme  accuracy  drop  weight 
may  be  determined.  On  the  other  hand,  by  the  method  of 
capillary  rise,  errors  may  occur  from  incorrect  readings  of 
the  volume  of  the  liquid,  the  non-uniformity  in  diameter  of 
the  tube,  and  incorrect  values  for  the  density  of  the  liquid. 
As  an  example  of  the  magnitude  of  the  first  error  a  few 

*Read  from  curve. 
1  Approximation. 


hi  obs. 

hz  (corrected). 

A3  from  curve. 

7.86 

8.00 

8.00 

7.69 

7-83 

7-85 

7-395 

7.525 

7-525 

7.24 

7-37 

7.385 

7-105 

7-23 

7-23 

6.96 

7.08 

7-075 

19 

determinations  on  water  by  Ramsay  and  Shields1  may  be 
cited. 

t. 

7-4 
19-3 
40.0 
50.0 
60.0 
70.0 

Here  is  a  correction  of  the  obseived  reading  of  over  il/2 
per  cent.  A  glance  through  the  literature  on  capillary  rise 
method  shows  widely  varying  results  among  the  most  accurate 
workers.  By  the  drop  weight  method,  knowing  the  value  of 
KB  for  the  tip,  surface  tensions  may  be  readily  duplicated, 
as  has  been  repeatedly  done  with  water  during  the  course  of 
this  investigation.  Hence  it  would  seem  that  the  surface 
tensions  given  in  this  paper  for  water,  ethyl  alcohol,  methyl 
alcohol  and  acetic  acid  are  the  most  correct  values  thus  far 
determined  under  saturated  air  conditions. 

The  splendid  results  on  water  obtained  by  Volkmann  and 
by  B  runner  by  capillary  rise  agree  very  closely  indeed  with 
surface  tension  results  obtained  by  drop  weight  method. 
As  regards  the  surface  tension  values  obtained  by  Ramsay 
and  Shields,  it  is  significant  that  the  higher  the  temperature 
at  which  the  drop  weight  is  determined  the  more  closely  do 
the  latter  results  agree  with  the  former.  Volkmann  as  well 
as  B  runner  worked  under  the  same  conditions  under  which 
this  investigation  was  carried  out,  namely,  saturated  air 
conditions;  Ramsay  and  Shields,  however,  excluded  air,  the 
pressure  being  that  of  the  vapor  pressure  of  the  liquid  itself. 
As  will  be  seen,  the  greatest  difference  is  with  water  at  the 
lower  temperatures;  this  is  to  be  expected  since  the  greater 
the  surface  tension,  the  greater  the  solubility  of  air  in  the 
liquid.  Naturally  enough  then,  the  higher  the  temperature 
at  which  the  drop  weight  is  determined  the  more  nearly 
should  the  Ramsay  and  Shields'  values  be  approached,  since 
the  conditions  under  which  they  worked  is  also  approached. 

1  Z.  physik.  Chem.,  12,  471  (1895). 


20 

As  will  be  seen,  the  results  by  the  two  methods  on  the  alcohols 
agree  satisfactorily  at  the  higher  temperature. 

What  has  been  said  in  regard  to  surface  tension  applies 
equally  as  well,  of  course,  to  tc  calculations,  since  drop  weight 
is  substituted  for  surface  tension  in  the  formula  of  Ramsay 
and  Shields.  Referring  to  the  tables  containing  tc  calcula- 
tions it  is  seen  here  again  that  the  higher  the  temperature  at 
which  drop  weight  is  determined  the  nearer  is  the  true  critical 
temperature  of  the  liquid  approached.  In  a  paper  by 
Morgan,1  it  was  shown  that  by  applying  the  method  of  least 
squares  to  the  function  values  ^-(M/J)^  obtained  by  Ramsay 
and  Shields  for  water,  ethyl  alcohol,  methyl  alcohol  and 
acetic  acid,  the  ciitical  temperature  of  these  associated 
liquids  could  be  calculated,  the  resulting  calculation  agreeing 
very  closely  with  the  observed  critical  temperature  values. 
The  functions  so  treated  had  a  range  of  temperature  of  not 
less  than  140°. 

In  this  work  it  was  hoped  that  by  applying  this  method  of 
least  squares  to  the  function  values  W(M/d)^  the  critical 
temperatures  of  these  liquids  could  be  calculated.  In  every 
case,  however,  the  method  has  failed.  The  function  values 
for  water  so  treated  give  the  equation, 

W(M/d)*  =  578.96— 1. 155'— 0-00052*2. 

In  Table  5  column  marked  "W(M/rf)J  calc. "  is  shown  how 
closely  this  equation  agrees  with  the  observed  values.  How- 
ever, as  Morgan2  has  shown,  the  coefficient  of  /  divided  by 
twice  the  coefficient  of  /2  gives  critical  temperature  less  6. 
As  is  seen,  the  coefficients  here  so  treated  give  an  absurd 
number. 

It  was  suspected  that  since  the  highest  temperature  at 
which  a  determination  by  this  method  can  be  made  is  several 
degrees  below  that  of  the  boiling  point  of  the  liquid,  the 
extrapolation  necessary  for  calculating  critical  temperature 
would  be  too  great.  This  is  clearly  shown  in  figuring  out  the 
function  values  necessary  for  correct  tc.  Assuming  579.22 

1  Jour.  Am.  Chem.  Soc.,  31,  March,  1909. 
*  Loc.  cit. 


21 

(the  observed  function  value  at  zero)  as  correct,  and  357  as 
the  critical  temperature  of  water  less  6,  the  theoretical 
equation  for  function  values  becomes, 

W(M/d)?  =  579.22 — 1.08172 — O.OOI522. 

In  Table  5  column  marked  "  W(M/cf)  theoretical"  is  given 
the  calculated  function  values  from  this  equation,  and  it  is 
seen  that  the  observed  values  agree  very  closely  at  high 
temperature. 

The  method  of  least  squares  was  next  applied  to  the 
function  values  for  water  from  o°-8o°  as  used  by  Morgan. 
The  resulting  equation  gave  just  as  absurd  value  for  critical 
temperature;  indeed,  it  showed  practically  a  linear  rela- 
tionship through  this  temperature  range.  The  drop  weight 
and  also  the  function  value  show  practically  a  linear  rela- 
tionship in  all  four  cases,  especially  at  the  lower  temperatures; 
there  is  a  slight  curve  in  each  case  as  the  boiling  point  of  the 
liquid  is  approached. 

An  equation  for  the  different  tc  values  for  water  was  worked 
out  according  to  the  method  of  least  squares  with  the  follow- 
ing result: 

tc  =  252.41   +  0.508^ — 0.00022523. 
When  357  is  substituted  for  t  here  tc  becomes  405. 

The  values  for  tc  from  50-80  were  treated  in  the  same 
manner  with  the  resulting  equation, 

tc  =  284.28  +  0.48952 — 0.007362. 

When  357  is  substituted  for  t  here  tc  becomes  365  thus 
showing  clearly  that  the  higher  values  are  necessary  for 
calculating  critical  temperature  of  associated  liquids. 

Many  other  possibilities  for  calculating  critical  tempera- 
ture were  tried  out  with  the  same  negative  results.  They 
all  showed,  however,  that  the  observed  function  values  agree 
with  the  theoretical,  and  hence  it  must  be  concluded  that  the 
extrapolation  is  too  great  even  when  treated  by  the  method 
of  least  squares. 


SUMMARY. 

The  results  of  this  investigation  may  be  summarized  as 
follows : 

1.  The    drop    weights    of    the    associated    liquids — water, 
ethyl   alcohol,    methyl   alcohol  and   acetic   acid   have   been 
accurately  determined  at  small  temperature  intervals  from 
zero  to  a  few  degrees  below  the  boiling  point. 

2.  It   has   been   shown   that   the   resulting   drop   weights 
transformed  into  surface  tensions  give   the  most  accurate 
values  for  same,    under  saturated  air  conditions,   thus  far 
determined. 

3.  Unlike  the  non-associated  liquids,  critical  temperature 
could  not  be  calculated  even  with  a  wide  range  of  temperature, 
still  higher  temperatures  are  necessary. 


BIOGRAPHY. 

A.  McD.  McAfee  was  born  in  Corsicana,  Texas,  September 
24,  1886.  He  entered  the  University  of  Texas  in  1904, 
taking  the  B.A.  degree  there  in  1908.  He  was  Fellow  in 
Chemistry  in  i9O7-'o8  and  the  following  two  years  he  was  a 
graduate  student  and  Tutor  in  Chemistry  in  the  University 
of  Texas.  In  the  fall  of  1910  he  entered  Columbia  Uni- 
versity as  Goldschmidt  Fellow  in  Chemistry.  His  major 
work  has  been  in  Physical  Chemistry. 


